Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and systems and, more particularly, to mechanisms and techniques for separating up- and down-going wave-fields based on multicomponent seismic data.
Discussion of the Background
Marine seismic data acquisition and processing generate a profile (image) of the geophysical structure (subsurface) under the seafloor. While this profile does not provide an accurate location for oil and gas reservoirs, it suggests, to those trained in the field, the presence or absence of the oil and/or gas reservoirs. Thus, providing a high-resolution image of the subsurface is an ongoing process for the exploration of natural resources.
During a seismic gathering process, as shown in FIG. 1, a vessel 110 tows plural detectors 112, which are disposed along a cable 114. Cable 114 together with its corresponding detectors 112 are sometimes referred to, by those skilled in the art, as a streamer 116. Vessel 110 may tow plural streamers 116 at the same time. Streamers may be disposed horizontally, i.e., lie at a constant depth z1 relative to the ocean surface 118. Also, plural streamers 116 may form a constant angle (i.e., the streamers may be slanted) with respect to the ocean surface as disclosed in U.S. Pat. No. 4,992,992, the entire content of which is incorporated herein by reference or the streamers may have a variable-depth profile as disclosed in U.S. Pat. No. 8,593,904, the entire content of which is incorporated herein by reference.
Still with reference to FIG. 1, vessel 110 may also tow a seismic source 120 configured to generate an acoustic wave 122a. Acoustic wave 122a propagates downward and penetrates the seafloor 124, eventually being reflected by a reflecting structure 126 (reflector R). Reflected acoustic wave 122b propagates upward and is detected by detector 112. For simplicity, FIG. 1 shows only two paths 122a corresponding to the acoustic wave. Parts of reflected acoustic wave 122b (primary or up-going) are recorded by various detectors 112 (recorded signals are called traces) while parts of reflected wave 122c pass detectors 112 and arrive at the water surface 118. Since the interface between the water and air is well approximated as a quasi-perfect reflector (i.e., the water surface acts as a mirror for acoustic waves), reflected wave 122c is reflected back toward detector 112 as shown by wave 122d in FIG. 1. Wave 122d is normally referred to as a ghost wave (or down-going wave). Ghosts are also recorded by detector 112, but with a reverse polarity and a time lag relative to primary wave 122b if the detector is a hydrophone. The degenerative effect that ghost arrival has on seismic bandwidth and resolution is known. In essence, interference between primary and ghost arrivals causes notches, or gaps, in the frequency content recorded by detectors.
The recorded traces may be used to image the subsurface (i.e., earth structure below surface 124) and to determine the position and presence of reflectors 126. However, ghosts disturb the accuracy of the final image of the subsurface and, for at least this reason, various methods exist for removing ghosts, i.e., deghosting, from the acquired seismic data. These methods were designed for deghosting seismic data h recorded with hydrophones, as described by the following equation:h=Lp  (1)or, in the expanded matrix form,
                                          (                                                                                h                    1                                                                                                                    h                    2                                                                                                                    h                    N                                                                        )                    ⁢                      (                                          e                                                      -                    2                                    ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                                      τ                    u                                                              +                              Re                                                      -                    2                                    ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                                      τ                    d                                                                        )                    ⁢                      (                                                                                p                    1                                                                                                                    p                    2                                                                                                                    p                    3                                                                                                                    p                    M                                                                        )                          ,                            (        2        )            where column vector h contains a frequency slice from the shot domain data (known), column vector p contains the surface datum tau-p model (unknown), matrix L makes the transform (known) from the surface tau-p model to the input shot data, and R is the free surface reflectivity (often taken to be −1). Matrix L combines in this case the operations of reverse tau-p transform, redatuming and reghosting.
The time shifts for primary (up-going) and ghost (down-going) wave fields are given by:τu=(on+Δo)sxm−Δτ  (3)τd=(on−Δo)sxm+Δτ,  (4)where on is the offset of a given trace in column vector h, sxm is the slowness in x-direction of a given trace in the surface tau-p model, Δo is the offset perturbation as described in U.S. Pat. 9,103,941 (the '941 patent), and Δt is the temporal perturbation as also described in the '941 patent. Equation (1) can be solved in the time or spectral (e.g., frequency) domain using linear inversion. The method can be applied on the whole shot (cable-by-cable) or in spatial windows of a user-defined number of channels.
However, existing methods relate to pressure measurements h made, for example, by hydrophones. Currently, the new streamer generation is capable of measuring not only pressure but also particle motion data, e.g., displacement, velocity, differential pressure, acceleration, etc. Thus, there is a desire to process not only pressure measurements, but also particle motion data. Accordingly, it would be desirable to provide systems and methods with such capabilities.